In a prior art machine of this general type, a plurality of processing heads are attached to a swiveling or rotatable disc which is disposed to be rotatable about a horizontal axis and which can be secured in certain swiveling positions by index pins. The index pins can either be attached solidly, as a result of which the swiveling disc must be shifted in an axial direction and, in addition to the securing of the position, a coupling of the operating head nearest to the processing location can be achieved with an operating spindle. Alternatively, the index pins and the coupling are axially shiftable so that an axial shifting of the swiveling disc is not necessary. The processing head coupled with the driving spindle can, in addition, be pressed against the housing of the machine. In a device of this type, the swiveling disc is difficult to align as a result of the swiveling process, since the masses which are to be moved will not permit a swiveling movement through a precisely determined sector angle. Moreover, the processing head, connected firmly to the swiveling disc, causes difficulties during the fixation in its operating position and in coupling with the driving spindle. An apparatus of this type is shown in German Offenlegungsschriften No. 19,31,559.